We show the existence of the stack of micro-differential modules on an arbitrary contact manifold, although we cannot expect the global existence of the ring of micro-differential operators.
Some structure properties of CQ*-algebras are investigated. The usual multiplication of a quasi *-algebra is generalized by introducing a weak- and strong product. The *-semisemplicity is defined via a suitable family of positive sesquilinear forms and some consequences of this notion are derived. The basic elements of a functional calculus on these partial algebraic structures are discussed.
A discrete model of the integer quantum Hall effect is analysed via its associated C*-algebra. The relationship with the usual continuous models is established by viewing the observable algebras of each as both twisted group C*-algebras and twisted cross products. A Fredholm module for the discrete model is presented, and its Chern character is calculated.
Let \mathscr{D}w' be the space of Beurling's generalized distributions on Rn and \mathscr{E}w' the spaces of generalized distributions which has compact support. We show that, for S ∈ \mathscr{E}w', S * \mathscr{D}w'=\mathscr{D}w' is equivalent to the following: Every generalized distribution u ∈ \mathscr{E}w' with S * u ∈ \mathscr{D}w is in \mathscr{D}w.